The perimeter of the triangle ABC will be 24.9. Then the correct option is C.
What is the distance between two points?
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x – h)² + (y – k)²
The vertices of the triangle are A(1, 3), B(11, 4), and C(7, 9).
The distance between AB will be
AB² = (11 – 1)² + (4 – 3)²
AB² = 101
AB = 10.05
The distance between BC will be
BC² = (11 – 7)² + (4 – 9)²
BC² = 41
BC = 6.40
The distance between AC will be
AC² = (7 – 1)² + (9 – 3)²
AC² = 72
AC = 8.50
Then the perimeter of the triangle ABC will be
Perimeter = AB + BC + CA
Perimeter = 10.05 + 6.40 + 8.50
Perimeter = 24.95 ≈ 24.9
The perimeter of the triangle ABC will be 24.9.
Then the correct option is C.
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